It is not necessary. People from a different time zone may not receive anything if nomination limit will be removed.
Then people may not know if you accidentally miss their request.

With the removal of the nomination limit, can't there be instances where a person can snatch all the games for their friends? I know it's one nomination per post and one has to wait at least 10 min before posting again, but it still can happen, especally due to the different time zones like Catac1ysm mentioned.

As for the "No more saying Granted or Denied", when you post the "Games delivered" message, would it be as a response to the quoted qualified requests or just a single post not quoting anyone?

Keep in mind that the person nominated has to still be eligible for the giveaway to receive a game. So it's no different than if that person were to ask for the game themselves. The nominations are meant to help out valued community members who don't always check giveaways and for people who do check them all the time to think about others.

It would be a simple line like "Games delivered" or something more along my Star Trek lines like:
"Coordinates locked. Energizing. Transport complete!"
But to answer your question, no I would not quote everyone as it would take quite a while for me to do so.

Captain on the bridge!

In my opinion the rules are there to help you, so you should have full liberty in setting them up to fit your commanding style. As a bonus, all of them make perfect sense to me.

I mostly like all these changes.

A couple of comments:
1) To address Catac1ysm's point, perhaps limit it to one nomination a day, but no monthly limit.
2) No need to wait 15 minutes, 11 is enough (as GOG uses a 10-minute gap).

I approve of - or am indifferent about - all the changes you propose.

I recommend starting the first post with the below bit from the current rules, slightly expanded (proposed extra bits underlined), so that people who're new have the highest chance of understanding what is going on.

It makes sense to optimize the time required for the operator. If it turns out that someone is using the adjusted set of rules for themselves or communication problems arise, you can always adjust the rules.

Definitely agree with the better "background checks", indifferent to a shorter version of the rules as long as that doesn't mean cutting any, or any clarifications, but personally disagree with the other two proposals.
In case of expiring keys the nomination limit should be lifted, but those fall under requirements waived anyway (and maybe we could even return to what moonshineshadow was doing and make calls for people to find users who want those games), but otherwise a person being able to "stand in" for several others doesn't seem quite right. That said, I guess mrkgnao's suggestion of one nomination per day would work, so active community members will generally have time to check the list before more nominations are made.
As for the granted or denied, on the one hand it's a confirmation for people that their request has been seen even if denied (and there have been some, very rare but non-zero, cases of missed requests), and if denied then the reason is also given, which is important, even if it's just that someone else beat them to it. What's not needed is a reply/quote, so maybe you could just lump them, like:
"Games delivered to [users].
Unfortunately beaten to it: [users].
Need more activity: [users].
Already got a game this month: [users].
Edited post: [users].
[other categories/reasons if needed]"
And this also allows for searching by username, if needed for future reference.
But, of course, it is your work going into it, so what we say are just opinions...

EDIT: Doc's later post pointed out a very good reason why even that lumping won't really work...

I would keep the rules as is. They seem to be working fine
If it ain't broke, don't fix them.

I guess we can say goodbye to even more people not thanking (publicly) those who have donated games that they have been chosen or are lucky to be gifted, as whether they were successful in acquiring said game they had asked for will be done in secret. And there have been numerous winners in countless giveaways that have failed or chosen not to thank those responsible. Which to some/most may seem trivial (and call me old-fashioned), but gratitude and politeness cost nothing...

Ok with everything, captain!

However, I would at least post which requests were rejected. Otherwise, you'll have to deal with a lot of messages of people asking about them.

Honestly, I prefer to leave things as they are and make minimal changes, if any.
If things have worked well for a long time, let them stay that way.
Likewise, I completely agree with what fellow @Ice_Mage says.

I agree with this.

I definitely agree with this, as there are a few repeat offenders I have noticed that only come here for the free games. And have wanted to call them out or identify them to those responsible. But not being a snitch prevents me from doing so...

Regarding posting granted/denied, this helps those of us who sometimes donate large quantities of games in one go to keep track of who was given what and makes it easier to check that the code was redeemed to the correct account.